- #1
ergospherical
- 1,073
- 1,367
- Homework Statement
- Determine the period of small oscillations, given that the disc rolls without slipping
- Relevant Equations
- N/A
A disc of radius has a smaller disc of radius removed. The resulting object has mass :
The centre of mass is a distance from the edge. The moment of inertia of the shape about the centre is therefore the moment of inertia about is If the angle through which the disc has rotated is denoted , then the centre of mass has velocity Therefore the kinetic energy of the body is Meanwhile, the height of the centre of mass when the body has rotated by is therefore the potential energy is . Overall I write the energy as The motion does not look simple harmonic, at least for finite . To investigate we can put and , and I assume also , which gives However in the solution manual they write ?